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Chapter 17. Modeling Pollutant

Formation

This chapter discusses the models available in FLUENT for modelingpollutant formation.

Information is presented in the following sections:

• Section 17.1: NOx Formation

• Section 17.2: Soot Formation

17.1 NOx Formation

The following sections present the theoretical background of NOx pre-diction and information about the usage of the NOx models employedby the solver.

• Section 17.1.1: Overview and Limitations

• Section 17.1.2: Governing Equations for NOx Transport

• Section 17.1.3: Thermal NOx Formation

• Section 17.1.4: Prompt NOx Formation

• Section 17.1.5: Fuel NOx Formation

• Section 17.1.6: NOx Formation by Reburning

• Section 17.1.7: NOx Formation in Turbulent Flows

• Section 17.1.8: Using the NOx Model

c© Fluent Inc. November 28, 2001 17-1

Modeling Pollutant Formation

17.1.1 Overview and Limitations

NOx emission consists of mostly nitric oxide (NO). Less significant arenitrogen oxide (NO2) and nitrous oxide (N2O). NOx is a precursor forphotochemical smog, contributes to acid rain, and causes ozone deple-tion. Thus, NOx is a pollutant. The FLUENT NOx model provides a toolto understand the sources of NOx production and to aid in the design ofNOx control measures.

NOx Modeling in FLUENT

The FLUENT NOx model provides the capability to model thermal,prompt, and fuel NOx formation as well as NOx consumption due toreburning in combustion systems. It uses rate models developed at theDepartment of Fuel and Energy, The University of Leeds, England aswell as from the open literature.

To predict NOx emission, FLUENT solves a transport equation for ni-tric oxide (NO) concentration. With fuel NOx sources, FLUENT solvesan additional transport equation for an intermediate species (HCN orNH3). The NOx transport equations are solved based on a given flowfield and combustion solution. In other words, NOx is postprocessedfrom a combustion simulation. It is thus evident that an accurate com-bustion solution becomes a prerequisite of NOx prediction. For example,thermal NOx production doubles for every 90 K temperature increasewhen the flame temperature is about 2200 K. Great care must be exer-cised to provide accurate thermophysical data and boundary conditioninputs for the combustion model. Appropriate turbulence, chemistry,radiation and other submodels must be applied.

To be realistic, one can only expect results to be as accurate as the inputdata and the selected physical models. Under most circumstances, NOx

variation trends can be accurately predicted but the NOx quantity itselfcannot be pinpointed. Accurate prediction of NOx parametric trends cancut down on the number of laboratory tests, allow more design variationsto be studied, shorten the design cycle, and reduce product developmentcost. That is truly the power of the FLUENT NOx model and, in fact,the power of CFD in general.

17-2 c© Fluent Inc. November 28, 2001

17.1 NOx Formation

The Formation of NOx in Flames

In laminar flames, and at the molecular level within turbulent flames,the formation of NOx can be attributed to four distinct chemical kineticprocesses: thermal NOx formation, prompt NOx formation, fuel NOx

formation, and reburning. Thermal NOx is formed by the oxidation ofatmospheric nitrogen present in the combustion air. Prompt NOx isproduced by high-speed reactions at the flame front, and fuel NOx isproduced by oxidation of nitrogen contained in the fuel. The reburningmechanism reduces the total NOx formation by accounting for the re-action of NO with hydrocarbons. The FLUENT NOx model is able tosimulate all four of these processes.

Restrictions on NOx Modeling

• You must use the segregated solver. The NOx models are notavailable with either of the coupled solvers.

• The NOx models cannot be used in conjunction with the premixedcombustion model.

17.1.2 Governing Equations for NOx Transport

FLUENT solves the mass transport equation for the NO species, tak-ing into account convection, diffusion, production and consumption ofNO and related species. This approach is completely general, being de-rived from the fundamental principle of mass conservation. The effect ofresidence time in NOx mechanisms, a Lagrangian reference frame con-cept, is included through the convection terms in the governing equationswritten in the Eulerian reference frame. For thermal and prompt NOx

mechanisms, only the NO species transport equation is needed:

∂

∂t(ρYNO) + ∇ · (ρ~vYNO) = ∇ · (ρD∇YNO) + SNO (17.1-1)

As discussed in Section 17.1.5, the fuel NOx mechanisms are more in-volved. The tracking of nitrogen-containing intermediate species is im-portant. FLUENT solves a transport equation for the HCN or NH3

species in addition to the NO species:



∂

∂t(ρYHCN) + ∇ · (ρ~vYHCN) = ∇ · (ρDYHCN) + SHCN (17.1-2)

∂

∂t(ρYNH3) + ∇ · (ρ~vYNH3) = ∇ · (ρDYNH3) + SNH3 (17.1-3)

where YHCN, YNH3, and YNO are mass fractions of HCN, NH3, and NOin the gas phase. The source terms SHCN, SNH3, and SNO are to bedetermined next for different NOx mechanisms.

17.1.3 Thermal NOx Formation

The formation of thermal NOx is determined by a set of highly temperature-dependent chemical reactions known as the extended Zeldovich mecha-nism. The principal reactions governing the formation of thermal NOx

from molecular nitrogen are as follows:

O + N2

k+1⇀↽ N + NO (17.1-4)

N + O2

k+2⇀↽ O + NO (17.1-5)

A third reaction has been shown to contribute, particularly at near-stoichiometric conditions and in fuel-rich mixtures:

N + OHk+3⇀↽ H + NO (17.1-6)

Thermal NOx Reaction Rates

The rate constants for these reactions have been measured in numer-ous experimental studies [21, 70, 162], and the data obtained from thesestudies have been critically evaluated by Baulch et al. [11] and Hanson


17.1 NOx Formation

and Salimian [88]. The expressions for the rate coefficients for Reac-tions 17.1-4–17.1-6 used in the NOx model are given below. These wereselected based on the evaluation of Hanson and Salimian [88].

k1 = 1.8 × 108e−38370/T m3/gmol-s (17.1-7)

k−1 = 3.8 × 107e−425/T m3/gmol-s (17.1-8)

k2 = 1.8 × 104Te−4680/T m3/gmol-s (17.1-9)

k−2 = 3.8 × 103Te−20820/T m3/gmol-s (17.1-10)

k3 = 7.1 × 107e−450/T m3/gmol-s (17.1-11)

k−3 = 1.7 × 108e−24560/T m3/gmol-s (17.1-12)

In the above expressions, k1, k2, and k3 are the rate constants for theforward reactions 17.1-4–17.1-6, respectively, and k−1, k−2, and k−3 arethe corresponding reverse rates.

The net rate of formation of NO via Reactions 17.1-4–17.1-6 is given by

d[NO]dt

= k1[O][N2] + k2[N][O2] + k3[N][OH] − k−1[NO][N]

− k−2[NO][O] − k−3[NO][H] (17.1-13)

where all concentrations have units of gmol/m3.

In order to calculate the formation rates of NO and N, the concentrationsof O, H, and OH are required.



The Quasi-Steady Assumption for [N]

The rate of formation of NOx is significant only at high temperatures(greater than 1800 K) because fixation of nitrogen requires the breakingof the strong N2 triple bond (dissociation energy of 941 kJ/gmol). Thiseffect is represented by the high activation energy of Reaction 17.1-4,which makes it the rate-limiting step of the extended Zeldovich mecha-nism. However, the activation energy for oxidation of N atoms is small.When there is sufficient oxygen, as in a fuel-lean flame, the rate of con-sumption of free nitrogen atoms becomes equal to the rate of its for-mation and therefore a quasi-steady state can be established. This as-sumption is valid for most combustion cases except in extremely fuel-richcombustion conditions. Hence the NO formation rate becomes

d[NO]dt

= 2k1[O][N2]

(1 − k−1k−2[NO]2

k1[N2]k2[O2]

)(1 + k−1[NO]

k2[O2]+k3[OH]

) (gmol/m3-s) (17.1-14)

Sensitivity of Thermal NOx to Temperature

From Equation 17.1-14 it is clear that the rate of formation of NO willincrease with increasing oxygen concentration. It also appears that ther-mal NO formation should be highly dependent on temperature but in-dependent of fuel type. In fact, based on the limiting rate described inEquation 17.1-7, thermal NOx production rate doubles for every 90 Ktemperature increase beyond 2200 K.

Decoupling NOx and Flame Calculations

In order to solve Equation 17.1-14, concentration of O atoms and thefree radical OH will be required in addition to concentration of stablespecies (i.e., O2, N2). Following the suggestion by Zeldovich, the thermalNOx formation mechanism can be decoupled from the main combustionprocess, by assuming equilibrium values of temperature, stable species,O atoms, and OH radicals. However, radical concentrations, O atomsin particular, are observed to be more abundant than their equilibriumlevels. The effect of partial equilibrium O atoms on NOx formation rate


17.1 NOx Formation

has been investigated [159] during laminar methane-air combustion. Theresults of these investigations indicate that the level of NOx emission canbe underpredicted by as much as 28% in the flame zone, when assumingequilibrium O-atom concentrations.

Determining O Radical Concentration

There has been little detailed study of radical concentration in indus-trial turbulent flames, but work [56] has demonstrated the existence ofthis phenomenon in turbulent diffusion flames. Presently, there is nodefinitive conclusion as to the effect of partial equilibrium on NOx for-mation rates in turbulent flames. Peters and Donnerhack [178] suggestthat partial equilibrium radicals can account for no more than a 25%increase in thermal NOx and that fluid dynamics has the dominant ef-fect on NOx formation rate. Bilger et al. [18] suggest that in turbulentdiffusion flames, the effect of O atom overshoot on NOx formation rateis very important.

In order to overcome this possible inaccuracy, one approach would beto couple the extended Zeldovich mechanism with a detailed hydrocar-bon combustion mechanism involving many reactions, species, and steps.This approach has been used previously for research purposes [156].However, long computer processing time has made the method econom-ically unattractive and its extension to turbulent flows difficult.

To determine the O radical concentration, FLUENT uses one of threeapproaches—the equilibrium approach, the partial equilibrium approach,and the predicted concentration approach—in recognition of the ongoingcontroversy discussed above.

Method 1: Equilibrium Approach

The kinetics of the thermal NOx formation rate is much slower thanthe main hydrocarbon oxidation rate, and so most of the thermal NOx

is formed after completion of combustion. Therefore, the thermal NOx

formation process can often be decoupled from the main combustionreaction mechanism and the NOx formation rate can be calculated byassuming equilibration of the combustion reactions. Using this approach,



the calculation of the thermal NOx formation rate is considerably sim-plified. The assumption of equilibrium can be justified by a reduction inthe importance of radical overshoots at higher flame temperature [55].According to Westenberg [265], the equilibrium O-atom concentrationcan be obtained from the expression

[O] = kp[O2]1/2 (17.1-15)

With kp included, this expression becomes

[O] = 3.97 × 105T−1/2[O2]1/2e−31090/T gmol/m3 (17.1-16)

where T is in Kelvin.

Method 2: Partial Equilibrium Approach

An improvement to method 1 can be made by accounting for third-bodyreactions in the O2 dissociation-recombination process:

O2 + M ⇀↽ O + O + M (17.1-17)

Equation 17.1-16 is then replaced by the following expression [255]:

[O] = 36.64T 1/2[O2]1/2e−27123/T gmol/m3 (17.1-18)

which generally leads to a higher partial O-atom concentration.

Method 3: Predicted O Approach

When the O-atom concentration is well-predicted using an advancedchemistry model (such as the flamelet submodel of the non-premixedmodel), [O] can be taken simply from the local O-species mass fraction.


17.1 NOx Formation

Determining OH Radical Concentration

FLUENT uses one of three approaches to determine the OH radical con-centration: the exclusion of OH from the thermal NOx calculation ap-proach, the partial equilibrium approach, and the use of the predictedOH concentration approach.

Method 1: Exclusion of OH Approach

In this approach, the third reaction in the extended Zeldovich mecha-nism (Equation 17.1-6) is assumed to be negligible through the followingobservation:

k2[O2]eq � k3[OH]eq

This assumption is justified for lean fuel conditions and is a reasonableassumption for most cases.

Method 2: Partial Equilibrium Approach

In this approach, the concentration of OH in the third reaction in theextended Zeldovich mechanism (Equation 17.1-6) is given by [12, 264]

[OH] = 2.129 × 102T−0.57e−4595/T [O]1/2[H2O]1/2 gmol/m3 (17.1-19)

Method 3: Predicted OH Approach

As in the predicted O approach, when the OH radical concentration iswell-predicted using an advanced chemistry model such as the flameletmodel, [OH] can be taken directly from the local OH species mass frac-tion.

Summary

To summarize, thermal NOx formation rate is predicted by Equation17.1-14. The O-atom concentration needed in Equation 17.1-14 is com-puted using Equation 17.1-16 for the equilibrium assumption, using



Equation 17.1-18 for a partial equilibrium assumption, or using the lo-cal O-species mass fraction. You will make the choice during problemsetup. In terms of the transport equation for NO (Equation 17.1-1), theNO source term due to thermal NOx mechanisms is

Sthermal,NO = Mw,NOd[NO]dt

(17.1-20)

where Mw,NO is the molecular weight of NO, and d[NO]/dt is computedfrom Equation 17.1-14.

17.1.4 Prompt NOx Formation

It is known that during combustion of hydrocarbon fuels, the NOx for-mation rate can exceed that produced from direct oxidation of nitrogenmolecules (i.e., thermal NOx).

Where and When Prompt NOx Occurs

The presence of a second mechanism leading to NOx formation was firstidentified by Fenimore [63] and was termed “prompt NOx”. There isgood evidence that prompt NOx can be formed in a significant quantityin some combustion environments, such as in low-temperature, fuel-richconditions and where residence times are short. Surface burners, stagedcombustion systems, and gas turbines can create such conditions [6].

At present the prompt NOx contribution to total NOx from stationarycombustors is small. However, as NOx emissions are reduced to verylow levels by employing new strategies (burner design or furnace geom-etry modification), the relative importance of the prompt NOx can beexpected to increase.

Prompt NOx Mechanism

Prompt NOx is most prevalent in rich flames. The actual formationinvolves a complex series of reactions and many possible intermediatespecies. The route now accepted is as follows:


17.1 NOx Formation

CH + N2 ⇀↽ HCN + N (17.1-21)

N + O2 ⇀↽ NO + O (17.1-22)

HCN + OH ⇀↽ CN + H2O (17.1-23)

CN + O2 ⇀↽ NO + CO (17.1-24)

A number of species resulting from fuel fragmentation have been sug-gested as the source of prompt NOx in hydrocarbon flames (e.g., CH,CH2, C, C2H), but the major contribution is from CH (Equation 17.1-21)and CH2, via

CH2 + N2 ⇀↽ HCN + NH (17.1-25)

The products of these reactions could lead to formation of amines andcyano compounds that subsequently react to form NO by reactions sim-ilar to those occurring in oxidation of fuel nitrogen, for example:

HCN + N ⇀↽ N2 + ..... (17.1-26)

Factors of Prompt NOx Formation

Prompt NOx formation is proportional to the number of carbon atomspresent per unit volume and is independent of the parent hydrocarbonidentity. The quantity of HCN formed increases with the concentrationof hydrocarbon radicals, which in turn increases with equivalence ratio.As the equivalence ratio increases, prompt NOx production increases atfirst, then passes a peak, and finally decreases due to a deficiency inoxygen.



Primary Reaction

Reaction 17.1-21 is of primary importance. In recent studies [201], com-parison of probability density distributions for the location of the peakNOx with those obtained for the peak CH have shown close correspon-dence, indicating that the majority of the NOx at the flame base isprompt NOx formed by the CH reaction. Assuming that Reaction 17.1-21controls the prompt NOx formation rate,

d[NO]dt

= k0[CH][N2] (17.1-27)

Modeling Strategy

There are, however, uncertainties about the rate data for the above re-action. From Reactions 17.1-21–17.1-25, it can be concluded that theprediction of prompt NOx formation within the flame requires couplingof the NOx kinetics to an actual hydrocarbon combustion mechanism.Hydrocarbon combustion mechanisms involve many steps and, as men-tioned previously, are extremely complex and costly to compute. In thepresent NOx model, a global kinetic parameter derived by De Soete [223]is used. De Soete compared the experimental values of total NOx forma-tion rate with the rate of formation calculated by numerical integrationof the empirical overall reaction rates of NOx and N2 formation. Heshowed that overall prompt formation rate can be predicted from theexpression

d[NO]dt

= (overall prompt NOx formation rate)

−(overall prompt N2 formation rate) (17.1-28)

In the early stages of the flame, where prompt NOx is formed underfuel-rich conditions, the O concentration is high and the N radical almostexclusively forms NOx rather than nitrogen. Therefore, the prompt NOx

formation rate will be approximately equal to the overall prompt NOx

formation rate:


17.1 NOx Formation

d[NO]dt

= kpr[O2]a[N2][FUEL]e−Ea/RT (17.1-29)

For C2H4 (ethylene)-air flames,

kpr = 1.2 × 107(RT/p)a+1

Ea = 60 kcal/gmol

where a is the oxygen reaction order, R is the universal gas constant, andp is pressure (all in SI units). The rate of prompt NOx formation is foundto be of the first order with respect to nitrogen and fuel concentration,but the oxygen reaction order, a, depends on experimental conditions.

Rate for Most Hydrocarbon Fuels

Equation 17.1-29 was tested against the experimental data obtained byBackmier et al. [4] for different mixture strengths and fuel types. Thepredicted results indicated that the model performance declined signif-icantly under fuel-rich conditions and for higher hydrocarbon fuels. Toreduce this error and predict the prompt NOx adequately in all condi-tions, the De Soete model was modified using the available experimentaldata. A correction factor, f , was developed, which incorporates the ef-fect of fuel type, i.e., number of carbon atoms, and air-to-fuel ratio forgaseous aliphatic hydrocarbons. Equation 17.1-29 now becomes

d[NO]dt

= fk′pr[O2]a[N2][FUEL]e−E′a/RT (17.1-30)

so that the source term due to prompt NOx mechanism is

Sprompt,NO = Mw,NOd[NO]dt

(17.1-31)

In the above equations,

f = 4.75 + 0.0819 n− 23.2φ + 32φ2 − 12.2φ3 (17.1-32)



n is the number of carbon atoms per molecule for the hydrocarbon fuel,and φ is the equivalence ratio. The correction factor is a curve fit for ex-perimental data, valid for aliphatic alkane hydrocarbon fuels (CnH2n+2)and for equivalence ratios between 0.6 and 1.6. For values outside therange, the appropriate limit should be used. Values of k′pr and E′

a areselected in accordance with reference [58].

Here the concept of equivalence ratio refers to an overall equivalenceratio for the flame, rather than any spatially varying quantity in theflow domain. In complex geometries with multiple burners this maylead to some uncertainty in the specification of φ. However, since thecontribution of prompt NOx to the total NOx emission is often verysmall, results are not likely to be biased significantly.

Oxygen Reaction Order

Oxygen reaction order depends on flame conditions. According to DeSoete [223], oxygen reaction order is uniquely related to oxygen molefraction in the flame:

a =

1.0, XO2 ≤ 4.1 × 10−3

−3.95 − 0.9 lnXO2 , 4.1 × 10−3 ≤ XO2 ≤ 1.11 × 10−2

−0.35 − 0.1 lnXO2 , 1.11 × 10−2 < XO2 < 0.030, XO2 ≥ 0.03

(17.1-33)

17.1.5 Fuel NOx Formation

Fuel-Bound N2

It is well known that nitrogen-containing organic compounds present inliquid or solid fossil fuel can contribute to the total NOx formed duringthe combustion process. This fuel nitrogen is a particularly importantsource of nitrogen oxide emissions for residual fuel oil and coal, whichtypically contain 0.3–2% nitrogen by weight. Studies have shown thatmost of the nitrogen in heavy fuel oils is in the form of heterocycles andit is thought that the nitrogen components of coal are similar [107]. It


17.1 NOx Formation

is believed that pyridine, quinoline, and amine type heterocyclic ringstructures are of importance.

Reaction Pathways

The extent of conversion of fuel nitrogen to NOx is dependent on the lo-cal combustion characteristics and the initial concentration of nitrogen-bound compounds. Fuel-bound nitrogen-containing compounds are re-leased into the gas phase when the fuel droplets or particles are heatedduring the devolatilization stage. From the thermal decomposition ofthese compounds, (aniline, pyridine, pyrroles, etc.) in the reaction zone,radicals such as HCN, NH3, N, CN, and NH can be formed and con-verted to NOx. The above free radicals (i.e., secondary intermediatenitrogen compounds) are subject to a double competitive reaction path.This chemical mechanism has been subject to several detailed investiga-tions [157]. Although the route leading to fuel NOx formation and de-struction is still not completely understood, different investigators seemto agree on a simplified model:

NO

NON2

Fuel Nitrogen Nitrogen Intermediates

O 2

oxidation

reduction

Recent investigations [94] have shown that hydrogen cyanide appears tobe the principal product if fuel nitrogen is present in aromatic or cyclicform. However, when fuel nitrogen is present in the form of aliphaticamines, ammonia becomes the principal product of fuel nitrogen conver-sion.

In the FLUENT NOx model, sources of NOx emission for gaseous, liq-uid and coal fuels are considered separately. The nitrogen-containingintermediates are grouped to be HCN or NH3 only. Two transport equa-tions (17.1-1 and 17.1-2 or 17.1-3) are solved. The source terms SHCN,



SNH3 , and SNO are to be determined next for different fuel types. Dis-cussions to follow refer only to fuel NOx sources for SNO. Contributionsfrom thermal and prompt mechanisms have been discussed in previoussections.

Fuel NOx from Gaseous and Liquid Fuels

The fuel NOx mechanisms for gaseous and liquid fuels are based ondifferent physics but the same chemical reaction pathways.

Fuel NOx from Intermediate Hydrogen Cyanide (HCN)

When HCN is used as the intermediate species:

Fuel Nitrogen

NO

2: NON2

1: O2

oxidation

reduction

HCN

The source terms in the transport equations can be written as follows:

SHCN = Spl,HCN + SHCN−1 + SHCN−2 (17.1-34)

SNO = SNO−1 + SNO−2 (17.1-35)

HCN Production in a Gaseous Fuel

The rate of HCN production is equivalent to the rate of combustion ofthe fuel:

Spl,HCN =Rcf YN,fuel Mw,HCN

Mw,N(17.1-36)


17.1 NOx Formation

where Spl,HCN = source of HCN (kg/m3-s)Rcf = mean limiting reaction rate of fuel (kg/m3-s)YN,fuel = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, Rcf , is calculated from the Mag-nussen combustion model, so the gaseous fuel NOx option is availableonly when the generalized finite-rate model is used.

HCN Production in a Liquid Fuel

The rate of HCN production is equivalent to the rate of fuel release intothe gas phase through droplet evaporation:

Spl,HCN =Sfuel YN,fuel Mw,HCN

Mw,NV(17.1-37)

where Spl,HCN = source of HCN (kg/m3-s)Sfuel = rate of fuel release from the

liquid droplets to the gas (kg/s)YN,fuel = mass fraction of nitrogen in the fuelV = cell volume (m3)

HCN Consumption

The HCN depletion rates from reactions (1) and (2) in the above mech-anism are the same for both gaseous and liquid fuels, and are given byDe Soete [223] as

R1 = A1 XHCN XaO2

e−E1/RT (17.1-38)

R2 = A2 XHCN XNO e−E2/RT (17.1-39)



where R1, R2 = conversion rates of HCN (s−1)T = instantaneous temperature (K)X = mole fractionsA1 = 3.5 ×1010 s−1

A2 = 3.0 ×1012 s−1

E1 = 67 kcal/gmolE2 = 60 kcal/gmol

The oxygen reaction order, a, is calculated from Equation 17.1-33.

Since mole fraction is related to mass fraction through molecular weightsof the species (Mw,i) and the mixture (Mw,m),

Xi = YiMw,m

Mw,i=

Yi

Mw,i

(ρRT

p

)(17.1-40)

HCN Sources in the Transport Equation

The mass consumption rates of HCN which appear in Equation 17.1-34are calculated as

SHCN−1 = −R1Mw,HCN p

RT(17.1-41)

SHCN−2 = −R2Mw,HCN p

RT(17.1-42)

where SHCN−1 = consumption rates of HCN inSHCN−2 reactions 1 and 2 respectively (kg/m3-s)p = pressure (Pa)T = mean temperature (K)R = universal gas constant

NOx Sources in the Transport Equation

NOx is produced in reaction 1 but destroyed in reaction 2. The sourcesfor Equation 17.1-35 are the same for a gaseous as for a liquid fuel, andare evaluated as follows:


17.1 NOx Formation

SNO−1 = −SHCN−1Mw,NO

Mw,HCN= R1

Mw,NO p

RT(17.1-43)

SNO−2 = SHCN−2Mw,NO

Mw,HCN= −R2

Mw,NO p

RT(17.1-44)

Fuel NOx from Intermediate Ammonia (NH3)

When NH3 is used as the intermediate species:

Fuel Nitrogen

NO

2: NON2

1: O2

oxidation

reduction

NH 3

The source terms in the transport equations can be written as follows:

SNH3 = Spl,NH3 + SNH3−1 + SNH3−2 (17.1-45)

SNO = SNO−1 + SNO−2 (17.1-46)

NH3 Production in a Gaseous Fuel

The rate of NH3 production is equivalent to the rate of combustion ofthe fuel:

Spl,NH3 =Rcf YN,fuel Mw,NH3

Mw,N(17.1-47)



where Spl,NH3 = source of NH3 (kg/m3-s)Rcf = mean limiting reaction rate of fuel (kg/m3-s)YN,fuel = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, Rcf , is calculated from the Mag-nussen combustion model, so the gaseous fuel NOx option is availableonly when the generalized finite-rate model is used.

NH3 Production in a Liquid Fuel

The rate of NH3 production is equivalent to the rate of fuel release intothe gas phase through droplet evaporation:

Spl,NH3 =Sfuel YN,fuel Mw,NH3

Mw,NV(17.1-48)

where Spl,NH3 = source of NH3 (kg/m3-s)Sfuel = rate of fuel release from the

liquid droplets to the gas (kg/s)YN,fuel = mass fraction of nitrogen in the fuelV = cell volume (m3)

NH3 Consumption

The NH3 depletion rates from reactions (1) and (2) in the above mech-anism are the same for both gaseous and liquid fuels, and are given byDe Soete [223] as

R1 = A1 XNH3 XaO2

e−E1/RT (17.1-49)

R2 = A2 XNH3 XNO e−E2/RT (17.1-50)


17.1 NOx Formation

where R1, R2 = conversion rates of NH3 (s−1)T = instantaneous temperature (K)X = mole fractionsA1 = 4.0 ×106 s−1

A2 = 1.8 ×106 s−1

E1 = 133.9 kJ/gmolE2 = 113 kJ/gmol

The oxygen reaction order, a, is calculated from Equation 17.1-33.

Since mole fraction is related to mass fraction through molecular weightsof the species (Mi) and the mixture (Mm),

Xi = YiMw,m

Mw,i=

Yi

Mw,i

(ρRT

p

)(17.1-51)

NH3 Sources in the Transport Equation

The mass consumption rates of NH3 which appear in Equation 17.1-45are calculated as

SNH3−1 = −R1Mw,NH3 p

RT(17.1-52)

SNH3−2 = −R2Mw,NH3 p

RT(17.1-53)

where SNH3−1 = consumption rates of NH3 inSNH3−2 reactions 1 and 2 respectively (kg/m3-s)p = pressure (Pa)T = mean temperature (K)R = universal gas constant

NOx Sources in the Transport Equation

NOx is produced in reaction 1 but destroyed in reaction 2. The sourcesfor Equation 17.1-46 are the same for a gaseous as for a liquid fuel, andare evaluated as follows:



SNO−1 = −SNH3−1Mw,NO

Mw,NH3

= R1Mw,NO p

RT(17.1-54)

SNO−2 = SNH3−2Mw,NO

Mw,NH3

= −R2Mw,NO p

RT(17.1-55)

Fuel NOx from Coal

Nitrogen in Char and in Volatiles

For the coal it is assumed that fuel nitrogen is distributed between thevolatiles and the char. Since there is no reason to assume that N isequally distributed between the volatiles and the char, we have allowedthe fraction of N in the volatiles and the char to be specified separately.

When HCN is used as the intermediate species, two variations of fuel NOx

mechanisms for coal are included. When NH3 is used as the intermediatespecies, two variations of fuel NOx mechanisms for coal are included,much like in the calculation of NOx production from the coal via HCN.It is assumed that fuel nitrogen is distributed between the volatiles andthe char.

Coal Fuel NOx Scheme A [222]

The first HCN mechanism assumes that all char N converts to HCNwhich is then converted partially to NO [222]. The reaction pathway isdescribed as follows:

HCN NO

Char N

Volatile N

2: NO

3: Char

N2

1: O2 N2


17.1 NOx Formation

With the first scheme, all char-bound nitrogen converts to HCN. Thus,

Schar,HCN =ScYN,charMw,HCN

Mw,NV(17.1-56)

Schar,NO = 0 (17.1-57)

where Sc = char burnout rate (kg/s)YN,char = mass fraction of nitrogen in charV = cell volume (m3)

Coal Fuel NOx Scheme B [144]

The second HCN mechanism assumes that all char N converts to NOdirectly [144]. The reaction pathway is described as follows:

HCN NO

Char N

Volatile N

2: NO

3: Char

N2

1: O2 N2

According to Lockwood [144], the char nitrogen is released to the gasphase as NO directly, mainly as a desorption product from oxidized charnitrogen atoms. If this approach is followed, then

Schar,HCN = 0 (17.1-58)

Schar,NO =ScYN,charMw,NO

Mw,NV(17.1-59)



Which HCN Scheme to Use?

The second HCN mechanism tends to produce more NOx emission thanthe first. In general, however, it is difficult to say which one outperformsthe other.

The source terms for the transport equations are

SHCN = Spvc,HCN + SHCN−1 + SHCN−2 (17.1-60)

SNO = Schar,NO + SNO−1 + SNO−2 + SNO−3 (17.1-61)

Source contributions SHCN−1, SHCN−2, SNO−1, and SNO−2 are describedpreviously. Therefore, only the heterogeneous reaction source, SNO−3,the char NOx source, Schar,NO, and the HCN production source, Spvc,HCN,need to be considered.

NOx Reduction on Char Surface

The heterogeneous reaction of NO reduction on the char surface has beenmodeled according to reference [134]:

R3 = A3e−E3/RT pNO (17.1-62)

where R3 = rate of NO reduction (gmol/m2BET-s)

pNO = mean NO partial pressure (atm)E3 = 34 kcal/gmolA3 = 230 gmol/m2

BET-s-atmT = mean temperature (K)

The partial pressure pNO is calculated using Dalton’s law:

pNO = XNO p

The rate of NO consumption due to reaction 3 will then be


17.1 NOx Formation

SNO−3 =csABETMw,NOR3

1000

where ABET = BET surface area (m2/kg)cs = concentration of particles (kg/m3)SNO−3 = NO consumption (kg/m3-s)

BET Surface Area

The heterogeneous reaction involving char is mainly an adsorption pro-cess whose rate is directly proportional to the pore surface area. Thepore surface area is also known as the BET surface area due to the re-searchers who pioneered the adsorption theory (Brunauer, Emmett andTeller [28]). For commercial adsorbents, the pore (BET) surface areasrange from 100,000 to 2 million square meters per kilogram, depend-ing on the microscopic structure. For coal, the BET area is typically25,000 m2/kg which is used as the default in FLUENT. The overall sourceof HCN (Spvc,HCN) is a combination of volatile contribution (Svol,HCN)and char contribution (Schar,HCN):

Spvc,HCN = Svol,HCN + Schar,HCN

HCN from Volatiles

The source of HCN from the volatiles is related to the rate of volatilerelease:

Svol,HCN =Svol YN,volMw,HCN

Mw,NV

where Svol = source of volatiles originating fromthe coal particles into the gas phase (kg/s)

YN,vol = mass fraction of nitrogen in the volatilesV = cell volume (m3)

Calculation of sources related to char-bound nitrogen depends on thefuel NOx scheme selection.



Coal Fuel NOx Scheme C [222]

The first NH3 mechanism assumes that all char N converts to NH3 whichis then converted partially to NO [222]. The reaction pathway is de-scribed as follows:

NH NO

Char N

Volatile N

2: NO

3: Char

N2

1: O2 N23

In this scheme, all char-bound nitrogen converts to NH3. Thus,

Schar,NH3 =ScYN,charMw,NH3

Mw,NV(17.1-63)

Schar,NO = 0 (17.1-64)

where Sc = char burnout rate (kg/s)YN,char = mass fraction of nitrogen in charV = cell volume (m3)

Coal Fuel NOx Scheme D [144]

The second NH3 mechanism assumes that all char N converts to NOdirectly [144]. The reaction pathway is described as follows:


17.1 NOx Formation

NH NO

Char N

Volatile N

2: NO

3: Char

N2

1: O2 N23

According to Lockwood [144], the char nitrogen is released to the gasphase as NO directly, mainly as a desorption product from oxidized charnitrogen atoms. If this approach is followed, then

Schar,NH3 = 0 (17.1-65)

Schar,NO =ScYN,charMw,NO

Mw,NV(17.1-66)

Which NH3 Scheme to Use?

The second NH3 mechanism tends to produce more NOx emission thanthe first. In general, however, it is difficult to say which one outperformsthe other.

The source terms for the transport equations are

SNH3 = Spvc,NH3 + SNH3−1 + SNH3−2 (17.1-67)

SNO = Schar,NO + SNO−1 + SNO−2 + SNO−3 (17.1-68)

Source contributions SNH3−1, SNH3−2, SNO−1, SNO−2, SNO−3, Schar,NO

are described previously. Therefore, only the NH3 production source,Spvc,NH3 , needs to be considered.



The overall production source of NH3 is a combination of volatile con-tribution (Svol,NH3), and char contribution (Schar,NH3):

Spvc,NH3 = Svol,NH3 + Schar,NH3 (17.1-69)

NH3 from Volatiles

The source of NH3 from the volatiles is related to the rate of volatilerelease:

Svol,NH3 =Svol YN,volMw,NH3

Mw,NV

where Svol = source of volatiles originating fromthe coal particles into the gas phase (kg/s)

YN,vol = mass fraction of nitrogen in the volatilesV = cell volume (m3)

Calculation of sources related to char-bound nitrogen depends on thefuel NOx scheme selection.

17.1.6 NOx Formation From Reburning

The reburning NO mechanism is a pathway whereby NO reacts withhydrocarbons and is subsequently reduced. In general:

CHi + NO → HCN + products (17.1-70)

Three reburn reactions are modeled by FLUENT for 1600 ≤ T ≤ 2100:

CH + NO k1→ HCN + O (17.1-71)

CH2 + NO k2→ HCN + OH (17.1-72)

CH3 + NO k3→ HCN + H2O (17.1-73)


17.1 NOx Formation

If the temperature is outside of this range, NO reburn will not be com-puted.

The rate constants for these reactions are taken from [23]:

k1 = 1 × 108 m3/gmol-s (17.1-74)k2 = 1.4 × 106e−550/T m3/gmol-s (17.1-75)

k3 = 2 × 105 m3/gmol-s (17.1-76)

The NO depletion rate due to reburn is expressed as

d[NO]dt

= −k1[CH][NO] − k2[CH2][NO] − k3[CH3][NO] (17.1-77)

and the source term for the reburning mechanism in the NO transportequation can be calculated as

Sreburning,NO = −Mw,NOd[NO]dt

(17.1-78)

To calculate the NO depletion rate due to reburning, FLUENT will ob-!tain the concentrations of CH, CH2, and CH3 from the species mass frac-tion results of the combustion calculation. For this reason, you shouldinclude these species in the problem definition (either in prePDF—fornon-premixed combustion calculations—or in FLUENT).

17.1.7 NOx Formation in Turbulent Flows

The kinetic mechanisms of NOx formation and destruction describedin the preceding sections have all been obtained from laboratory experi-ments using either a laminar premixed flame or shock-tube studies wheremolecular diffusion conditions are well defined. In any practical combus-tion system, however, the flow is highly turbulent. The turbulent mixingprocess results in temporal fluctuations in temperature and species con-centration which will influence the characteristics of the flame.



The relationships among NOx formation rate, temperature, and speciesconcentration are highly nonlinear. Hence, if time-averaged compositionand temperature are employed in any model to predict the mean NOx for-mation rate, significant errors will result. Temperature and compositionfluctuations must be taken into account by considering the probabilitydensity functions which describe the time variation.

The Turbulence-Chemistry Interaction Model

In turbulent combustion calculations, FLUENT solves the density-weightedtime-averaged Navier-Stokes equations for temperature, velocity, andspecies concentrations or mean mixture fraction and variance. To cal-culate NO concentration, a time-averaged NO formation rate must becomputed at each point in the domain using the averaged flow-field in-formation.

Methods of modeling the mean turbulent reaction rate can be basedon either moment methods [268] or probability density function (PDF)techniques [102]. FLUENT uses the PDF approach.

The PDF method described here applies to the NOx transport equations!only. The preceding combustion simulation can use either the generalizedfinite rate chemistry model by Magnussen and Hjertager or the non-premixed combustion model. For details on these combustion models,please see Chapters 13 and 14.

The PDF Approach

The PDF method has proven very useful in the theoretical descriptionof turbulent flow [103]. In the FLUENT NOx model, a single- or joint-variable PDF in terms of a normalized temperature, species mass frac-tion, or the combination of both is used to predict the NOx emission. Ifthe non-premixed combustion model is used to model combustion, thena one- or two-variable PDF in terms of mixture fraction(s) is also avail-able. The mean values of the independent variables needed for the PDFconstruction are obtained from the solution of the transport equations.


17.1 NOx Formation

General Expression for Mean Reaction Rate

The mean turbulent reaction rate w can be described in terms of theinstantaneous rate w and a single or joint PDF of various variables. Ingeneral,

w =∫

· · ·∫w(V1, V2, . . .)P (V1, V2, . . .)dV1dV2 . . . (17.1-79)

where V1, V2,... are temperature and/or the various species concentra-tions present. P is the probability density function (PDF).

Mean Reaction Rate Used in FLUENT

The PDF is used for weighting against the instantaneous rates of pro-duction of NO (e.g., Equation 17.1-20) and subsequent integration oversuitable ranges to obtain the mean turbulent reaction rate. Hence wehave

SNO =∫SNO(V1)P1(V1)dV1 (17.1-80)

or, for two variables

SNO =∫ ∫

SNO(V1, V2, )P (V1, V2)dV1dV2 (17.1-81)

where SNO is the mean turbulent rate of production of NO, SNO is the in-stantaneous rate of production given by, for example, Equation 17.1-20,and P1(V1) and P (V1, V2) are the PDFs of the variables V1 and, if rele-vant, V2. The same treatment applies for the HCN or NH3 source terms.

Equation 17.1-80 or 17.1-81 must be integrated at every node and atevery iteration. For a PDF in temperature, the limits of integration aredetermined from the minimum and maximum values of temperature inthe combustion solution. For a PDF in mixture fraction, the limits ofthe integrations in Equation 17.1-80 or 17.1-81 are determined from thevalues stored in the look-up tables.



Statistical Independence

In the case of the two-variable PDF, it is further assumed that the vari-ables V1 and V2 are statistically independent so that P (V1, V2) can beexpressed as

P (V1, V2) = P1(V1)P2(V2) (17.1-82)

Beta PDF Assumed

P is assumed to be a two-moment beta function as appropriate for com-bustion calculations [87, 158]. The equation for the beta function is

P (V ) =Γ(α+ β)Γ(α)Γ(β)

V α−1(1−V )β−1 =V α−1(1 − V )β−1∫ 1

0V α−1(1 − V )β−1dV

(17.1-83)

where Γ( ) is the Gamma function, α and β depend on m, the meanvalue of the quantity in question, and its variance, σ2:

α = m

(m(1 −m)

σ2− 1

)(17.1-84)

β = (1 −m)(m(1 −m)

σ2− 1

)(17.1-85)

The beta function requires that the independent variable V assume val-ues between 0 and 1. Thus, field variables such as temperature must benormalized.

Calculation Method for σ2

The variance, σ2, can be computed by solving a transport equationduring the combustion calculation stage. This approach is compute-intensive and is not applicable for a postprocessing treatment of NOx


17.1 NOx Formation

prediction. Instead, calculation of σ2 is based on an approximate formof the variance transport equation.

A transport equation for the variance σ2 can be derived:

∂

∂t

(ρσ2

)+∇· (ρ~vσ2) = ∇

(µt

σt∇σ2

)+Cgµt(∇m)2−Cdρ

ε

kσ2 (17.1-86)

where the constants σt, Cg and Cd take the values 0.85, 2.86, and 2.0,respectively. Assuming equal production and dissipation of variance, onegets

σ2 =µt

ρ

k

ε

Cg

Cd(∇m)2 =

µt

ρ

k

ε

Cg

Cd

[(∂m

∂x

)2

+(∂m

∂y

)2

+(∂m

∂z

)2]

(17.1-87)

The term in the brackets is the dissipation rate of the independent vari-able.

For a PDF in mixture fraction, the mixture fraction variance has alreadybeen solved as part of the basic combustion calculation, so no additionalcalculation for σ2 is required.

17.1.8 Using the NOx Model

Decoupled Analysis: Overview

NOx concentrations generated in combustion systems are generally low.As a result, NOx chemistry has negligible influence on the predictedflow field, temperature, and major combustion product concentrations.It follows that the most efficient way to use the NOx model is as apostprocessor to the main combustion calculation.

The recommended procedure is as follows:

1. Calculate your combustion problem using FLUENT as usual.



2. Activate the desired NOx models (thermal, fuel, and/or promptNOx, with or without reburn) and set the appropriate parameters,as described in this section.

Define −→ Models −→ Pollutants −→NOx...

3. In the Solution Controls panel, turn off solution of all variablesexcept species NO and, if the fuel NOx submodel is activated,HCN or NH3.

Solve −→ Controls −→Solution...

4. Also in the Solution Controls panel, set a suitable value for the NO(and HCN or NH3, if appropriate) under-relaxation. A value of0.8 to 1.0 is suggested, although lower values may be required forcertain problems. That is, if convergence cannot be obtained, trya lower under-relaxation value.

5. In the Residual Monitors panel, decrease the convergence criterionfor NO (and HCN or NH3, if appropriate) to 10−6.

Solve −→ Monitors −→Residual...

6. Perform calculations until convergence (i.e., until the NO (andHCN or NH3, if solved) species residuals are below 10−6) to en-sure that the NO and HCN or NH3 concentration fields are nolonger evolving.

7. Review the mass fractions of NO (and HCN or NH3) with alphanu-merics and/or graphics tools in the usual way.

8. Save a new set of case and data files, if desired.

Inputs specific to the calculation of NOx formation are explained in theremainder of this section.

Activating the NOx Models

To activate the NOx models and set related parameters, you will use theNOx Model panel (Figure 17.1.1).

Define −→ Models −→ Pollutants −→NOx...


17.1 NOx Formation

Figure 17.1.1: The NOx Model Panel



Under Models, select the NOx models to be used in the calculation ofthe NO and HCN concentrations:

• To enable thermal NOx, turn on the Thermal NO option.

• To enable prompt NOx, turn on the Prompt NO option.

• To enable fuel NOx, turn on the Fuel NO option.

• To enable NO reburn, turn on the Reburn option. (Note that theReburn option will not appear until you have activated one of theother NO models listed above.)

Your selection(s) for Models will activate the calculation of thermal,prompt, and/or fuel NO, with or without reburn, in accordance withthe chemical kinetic models described in Sections 17.1.3–17.1.6. MeanNO formation rates will be computed directly from mean concentrationsand temperature in the flow field.

Setting Thermal NOx Parameters

The NOx routines employ three methods for calculation of thermal NOx

(as described in Section 17.1.3). You will specify the method to be usedin the NOx Model panel, under Thermal NO Parameters:

• To choose the equilibrium method, select Equilibrium in the [O]Model drop-down list.

• To choose the partial equilibrium method, select Partial-equilibriumin the [O] Model or [OH] Model drop-down list.

• To use the predicted O and/or OH concentration, select Instanta-neous in the [O] Model or [OH] Model drop-down list.

Setting Prompt NOx Parameters

Prompt NO formation is predicted using Equations 17.1-30 and 17.1-32.The parameters are entered under Prompt NO Parameters in the NOxModel panel:


17.1 NOx Formation

• Specify which of the defined species is the fuel by choosing it inthe Fuel Species drop-down list.

• Set the Fuel Carbon Number (number of carbon atoms per fuelmolecule)

• Set the Equivalence Ratio:

Equivalence Ratio =actual air-to-fuel ratio

stoichiometric air-to-fuel ratio

Setting Fuel NOx Parameters

For fuel NOx models, you will first need to specify the fuel type underFuel NO Parameters:

• For gaseous fuel NOx, select Gas under Fuel Type.

• For liquid fuel NOx, select Liquid under Fuel Type.

• For solid fuel NOx, select Solid under Fuel Type.

Note that you can use only one of the fuel models at a time.

Setting Gaseous and Liquid Fuel NOx Parameters

If you have selected Gas or Liquid as the Fuel Type under Fuel NO Pa-rameters, you will also need to specify the following:

• Select the intermediate species (HCN or NH3) in the N Intermediatedrop-down list.

• Set the correct mass fraction of nitrogen in the fuel (kg nitrogenper kg fuel) in the Fuel N Mass Fraction field

FLUENT will use Equations 17.1-34 and 17.1-35 (for HCN) or Equa-tions 17.1-45 and 17.1-46 (for NH3) to predict NO formation for a gaseousor liquid fuel.



Setting Solid (Coal) Fuel NOx Parameters

For solid fuel, FLUENT will use Equations 17.1-60 and 17.1-61 (for HCN)or Equations 17.1-67 and 17.1-68 (for NH3) to predict NO formation.Several inputs (under Fuel NO Parameters) are required for the coal fuelNOx model:

• Select the intermediate species (HCN or NH3) in the N Intermediatedrop-down list.

• Specify the mass fraction of nitrogen in the volatiles and in thechar in the Volatile N Mass Fraction and Char N Mass Fraction fields,respectively.

• Define the BET internal pore surface area (see Section 17.1.5 fordetails) of the particles in the BET Surface Area field.

• Select the char N conversion path from the Char N Conversion drop-down list as NO, HCN, or NH3. Note that HCN or NH3 can be se-lected only if the same species has been selected as the intermediatespecies in the N Intermediate drop-down list.

Setting Parameters for NOx Reburn

There are no special parameters to specify for the NOx reburn model.When you use this model, however, you must be sure to include thespecies CH, CH2, and CH3 in your problem definition, as warned in theReburn Parameters section of the NOx Model panel. See Section 17.1.6for details.

Setting Turbulence Parameters

If you want to take into account turbulent fluctuations (as described inSection 17.1.7) when you compute the specified NO formation (thermal,prompt, and/or fuel, with or without reburn), select one of the optionsin the PDF Mode drop-down list under Turbulence Interaction.

• Select Temperature to take into account fluctuations of tempera-ture.


17.1 NOx Formation

• Select Temperature/Species to take into account fluctuations oftemperature and mass fraction of the species selected in the Speciesdrop-down list (which appears when you select this option).

• Select Species 1/Species 2 to take into account the fluctuation ofmass fractions of two species selected in the Species 1 and Species 2drop-down lists (which appear when you select this option).

• (non-premixed combustion calculations only) Select Mixture Frac-tion to take into account fluctuation in the mixture fraction(s).

The Mixture Fraction option is available only if you are using the non-premixed combustion model to model the reacting system. If the Mix-ture Fraction option is used, the instantaneous temperatures, density,and species concentrations are taken from the PDF look-up table (cre-ated by prePDF) as a function of mixture fraction. The beta PDF inmixture fraction is calculated from the values of mean mixture fractionand variance at each cell. After the instantaneous NOx rates have beencalculated at each cell, they are convoluted with the mixture fractionPDF to yield the mean rates in turbulent flow.

Extra Input for Non-Adiabatic Non-Premixed Combustion CalculationsUsing a PDF in Mixture Fraction

If you choose the Mixture Fraction option and you are using the non-adiabatic non-premixed combustion model, an additional option (UseTop Temperature) will appear under Turbulence Interaction. When thisoption is off (the default condition) the local cell enthalpy is used to cal-culate the instantaneous temperature used in the NOx rate calculation.This option should be used in most cases. If you enable Use Top Temper-ature, then in the part of the domain where the turbulent fluctuationsare significant, the instantaneous temperatures are calculated in termsof the lowest heat loss (or highest heat gain) in that part of the domain.(In the equations in Section 14.1.2, the heat loss/gain is H∗.) The re-sult of this calculation will be the maximum possible NOx productionthat can be calculated through the convolution with the mixture frac-tion PDF. By comparing the default results with those generated usingthe top temperature option, you can determine how sensitive the NOx



calculation is to the local enthalpy variation when the fluctuations aresignificant.

Number of Beta Points

You can, optionally, adjust the number of Beta PDF Points. The defaultvalue of 10, indicating that the beta function in Equation 17.1-80 orEquation 17.1-81 will be integrated at 10 points on a histogram basis, willyield an accurate solution with reasonable computation time. Increasingthis value may improve accuracy, but will also increase the computationtime.

Specifying a User-Defined Function for the NOx Rate

You can, optionally, choose to specify a user-defined function for therate of NOx production. The rate returned from the UDF is addedto the rate returned from the standard NOx production options, if anyare selected. You can also choose to deselect all of the standard NOx

production options and use only the UDF rate.

Select the desired function in the NOx Rate drop-down list under User-Defined Functions. See the separate UDF Manual for details about user-defined functions.

Postprocessing

When you compute NOx formation, the following additional variableswill be available for postprocessing:

• Mass fraction of NO

• Mass fraction of HCN (appropriate fuel NOx model only)

• Mass fraction of NH3 (appropriate fuel NOx model only)

• Mole fraction of NO

• Mole fraction of HCN (appropriate fuel NOx model only)

• Mole fraction of NH3 (appropriate fuel NOx model only)


17.2 Soot Formation

• Concentration of NO

• Concentration of HCN (appropriate fuel NOx model only)

• Concentration of NH3 (appropriate fuel NOx model only)

• Variance of Temperature (variance of normalized temperature)

These variables are contained in the NOx... category of the variableselection drop-down list that appears in postprocessing panels.

17.2 Soot Formation

Information about soot formation is presented in the following sections:

• Section 17.2.1: Overview and Limitations

• Section 17.2.2: Theory

• Section 17.2.3: Using the Soot Models

17.2.1 Overview and Limitations

FLUENT provides two empirical models for the prediction of soot forma-tion in combustion systems. In addition, the predicted soot concentra-tion can be included in the prediction of radiation absorption coefficientswithin the combustion system. You can include the effect of soot on ra-diation absorption when you use the P-1, discrete ordinates, or discretetransfer radiation model with a variable absorption coefficient.

Predicting Soot Formation

FLUENT predicts soot concentrations in a combustion system using oneof two available models:

• the single-step Khan and Greeves model [113], in which FLUENTpredicts the rate of soot formation based on a simple empiricalrate.



• the two-step Tesner model [149, 242], in which FLUENT predictsthe formation of nuclei particles, with soot formation on the nuclei.

The Khan and Greeves model is the default model used by FLUENT whenyou include soot formation. In both models, combustion of the soot (andparticle nuclei) is assumed to be governed by the Magnussen combustionrate [149]. Note that this limits the use of the soot formation modelsto turbulent flows. Soot formation cannot be predicted by FLUENT forlaminar or inviscid flows.

Both soot formation models are empirically-based, approximate mod-els of the soot formation process in combustion systems. The detailedchemistry and physics of soot formation are quite complex and are onlyapproximated in the models used by FLUENT. You should view the re-sults of these models as qualitative indicators of your system performanceunless you can undertake experimental validation of the results.

Restrictions on Soot Modeling

The following restrictions apply to soot formation models:

• You must use the segregated solver. The soot models are not avail-able with either of the coupled solvers.

• Soot formation can be modeled only for turbulent flows.

• The soot model cannot be used in conjunction with the premixedcombustion model.

17.2.2 Theory

The Single-Step Soot Formation Model

In the single-step Khan and Greeves model [113], FLUENT solves a singletransport equation for the soot mass fraction:

∂

∂t(ρYsoot) + ∇ · (ρ~vYsoot) = ∇ ·

(µt

σsoot∇Ysoot

)+ Rsoot (17.2-1)


17.2 Soot Formation

whereYsoot = soot mass fractionσsoot = turbulent Prandtl number for soot transportRsoot = net rate of soot generation (kg/m3-s)

Rsoot, the net rate of soot generation, is the balance of soot formation,Rsoot,form, and soot combustion, Rsoot,comb:

Rsoot = Rsoot,form −Rsoot,comb (17.2-2)

The rate of soot formation is given by a simple empirical rate expression:

Rsoot,form = Cspfuelφre−E/RT (17.2-3)

whereCs = soot formation constant (kg/N-m-s)pfuel = fuel partial pressure (Pa)φ = equivalence ratior = equivalence ratio exponentE/R = activation temperature (K)

The rate of soot combustion is the minimum of two rate expressions [149]:

Rsoot,comb = min[R1, R2] (17.2-4)

The two rates are computed as

R1 = AρYsootε

k(17.2-5)

and

R2 = Aρ

(Yox

νsoot

)(Ysootνsoot

Ysootνsoot + Yfuelνfuel

)ε

k(17.2-6)



whereA = constant in the Magnussen modelYox, Yfuel = mass fractions of oxidizer and fuelνsoot, νfuel = mass stoichiometries for soot and fuel combustion

The default constants for the single-step model are valid for a wide rangeof hydrocarbon fuels.

The Two-Step Soot Formation Model

The two-step Tesner model [242] predicts the generation of radical nucleiand then computes the formation of soot on these nuclei. FLUENT thussolves transport equations for two scalar quantities: the soot mass frac-tion (Equation 17.2-1) and the normalized radical nuclei concentration:

∂

∂t(ρb∗nuc) + ∇ · (ρ~vb∗nuc) = ∇ ·

(µt

σnuc∇b∗nuc

)+ R∗

nuc (17.2-7)

whereb∗nuc = normalized radical nuclei concentration

(particles ×10−15/kg)σnuc = turbulent Prandtl number for nuclei transportR∗

nuc = normalized net rate of nuclei generation(particles ×10−15/m3-s)

In these transport equations, the rates of nuclei and soot generation arethe net rates, involving a balance between formation and combustion.

Soot Generation Rate

The two-step model computes the net rate of soot generation, Rsoot, inthe same way as the single-step model, as a balance of soot formationand soot combustion:

Rsoot = Rsoot,form −Rsoot,comb (17.2-8)

In the two-step model, however, the rate of soot formation, Rsoot,form,depends on the concentration of radical nuclei, cnuc:


17.2 Soot Formation

Rsoot,form = mp(α− βNsoot)cnuc (17.2-9)

wheremp = mean mass of soot particle (kg/particle)Nsoot = concentration of soot particles (particles/m3)cnuc = radical nuclei concentration = ρbnuc (particles/m3)α = empirical constant (s−1)β = empirical constant (m3/particle-s)

The rate of soot combustion, Rsoot,comb, is computed in the same way asfor the single-step model, using Equations 17.2-4–17.2-6.

The default constants for the two-step model are for combustion of acety-lene (C2H2). According to [1], these values should be modified for otherfuels, since the sooting characteristics of acetylene are known to be dif-ferent from those of saturated hydrocarbon fuels.

Nuclei Generation Rate

The net rate of nuclei generation in the two-step model is given by thebalance of the nuclei formation rate and the nuclei combustion rate:

R∗nuc = R∗

nuc,form −R∗nuc,comb (17.2-10)

whereR∗

nuc,form = rate of nuclei formation (particles ×10−15/m3-s)R∗

nuc,comb = rate of nuclei combustion (particles ×10−15/m3-s)

The rate of nuclei formation, R∗nuc,form, depends on a spontaneous for-

mation and branching process, described by

R∗nuc,form = η0 + (f − g)c∗nuc − g0c

∗nucNsoot (17.2-11)

η0 = a∗0cfuele−E/RT (17.2-12)



wherec∗nuc = normalized nuclei concentration (= ρb∗nuc)a∗0 = a0/1015

a0 = pre-exponential rate constant (particles/kg-s)cfuel = fuel concentration (kg/m3)f − g = linear branching − termination coefficient (s−1)g0 = linear termination on soot particles (m3/particle-s)

Note that the branching term, (f−g)c∗nuc, in Equation 17.2-11 is includedonly when the kinetic rate, η0, is greater than the limiting formation rate(105 particles/m3-s, by default).

The rate of nuclei combustion is assumed to be proportional to the rateof soot combustion:

R∗nuc,comb = Rsoot,comb

b∗nuc

Ysoot(17.2-13)

where the soot combustion rate, Rsoot,comb, is given by Equation 17.2-4.

Effect of Soot on the Radiation Absorption Coefficient

A description of the modeling of soot-radiation interaction is providedin Section 11.3.8.

17.2.3 Using the Soot Models

To compute the soot formation, you will need to start from a convergedfluid-flow solution. The procedure for setting up and solving a sootformation model is outlined below, and described in detail on the pagesthat follow. Remember that only the steps that are pertinent to sootmodeling are shown here. For information about inputs related to othermodels that you are using in conjunction with the soot formation model,see the appropriate sections for those models.

1. Calculate your turbulent combustion (finite-rate or non-premixed)problem using FLUENT as usual.


17.2 Soot Formation

2. Enable the desired soot formation model and set the related pa-rameters, as described in this section.

Define −→ Models −→ Pollutants −→Soot...

3. In the Solution Controls panel, turn off solution of all variablesexcept soot (and nuclei, if you are using the two-step model).

Solve −→ Controls −→Solution...

4. Also in the Solution Controls panel, set a suitable value for the soot(and nuclei, for the two-step model) under-relaxation factor(s). Avalue of 0.8 is suggested, although a lower value may be requiredfor certain problems. That is, if convergence cannot be obtained,try a lower under-relaxation value.

5. In the Residual Monitors panel, decrease the convergence criterionfor soot (and nuclei, for the two-step model) to 10−5.

Solve −→ Monitors −→Residual...

6. Define the boundary conditions for soot (and nuclei, for the two-step model) at flow inlets.

Define −→Boundary Conditions...

7. Perform calculations until convergence (i.e., until the soot—andnuclei, for the two-step model—residual is below 10−5) to ensurethat the soot (and nuclei) field is no longer evolving.

8. Review the mass fraction of soot (and nuclei) with alphanumericsand/or graphics tools in the usual way.

9. Save a new set of case and data files, if desired.

10. If you want to calculate a coupled solution for the soot and theflow field, turn on the other variables again and recompute untilconvergence. (See the end of this section for some advice on coupledcalculations.)



Selecting the Soot Model

You can enable the calculation of soot formation by selecting a sootmodel in the Soot Model panel (Figure 17.2.1).

Define −→ Models −→ Pollutants −→Soot...

Figure 17.2.1: The Soot Model Panel

Under Soot Formation Model, select either the One-Step or the Two-Stepmodel. The panel will expand to show the appropriate inputs for theselected model.

(If you want to include the effects of soot formation on the radiationabsorption coefficient, turn on the Generalized Model option under Soot-Radiation Interaction.)


17.2 Soot Formation

Setting the Combustion Process Parameters

For both soot models, you will next define the Process Parameters, whichdepend on the combustion process that you are modeling. These inputsinclude the stoichiometry of the fuel and soot combustion and (for thetwo-step model only) the average size and density of the soot particles:

Mean Diameter of Soot Particle and Mean Density of Soot Particle are theassumed average diameter and average density of the soot particlesin the combustion system, used to compute the soot particle mass,mp, in Equation 17.2-9 for the two-step model. Note that thedefault values for soot density and diameter are taken from [149].

These parameters will not appear when the one-step model is used.

Stoichiometry for Soot Combustion is the mass stoichiometry, νsoot, inEquation 17.2-6, which computes the soot combustion rate in bothsoot models. The default value supplied by FLUENT (2.6667) as-sumes that the soot is pure carbon and that the oxidizer is O2.

Stoichiometry for Fuel Combustion is the mass stoichiometry, νfuel, in Equa-tion 17.2-6, which computes the soot combustion rate in both sootmodels. The default value supplied by FLUENT (3.6363) is forcombustion of propane (C3H8) by oxygen (O2).

Defining the Fuel and Oxidizing Species

In addition to defining the stoichiometry for the fuel and soot combus-tion, you need to tell FLUENT which chemical species in your modelshould be used as the fuel and oxidizer. In the Soot Model panel un-der Species Definition, select the fuel in the Fuel drop-down list and theoxidizer in the Oxidant drop-down list.

If you are using the non-premixed model for the combustion calculationand your fuel stream, as defined in prePDF, consists of a mixture ofcomponents, you should choose the most appropriate species as the Fuelspecies for the soot formation model. Similarly, the most significantoxidizing component (e.g., O2) should be selected as the Oxidant.



Setting Model Parameters for the Single-Step Model

When you choose the single-step model for soot formation, the modelingparameters to be defined are those used in Equations 17.2-3, 17.2-5, and17.2-6:

Soot Formation Constant is the parameter Cs in Equation 17.2-3.

Equivalence Ratio Exponent is the exponent r in Equation 17.2-3.

Equivalence Ratio Minimum and Equivalence Ratio Maximum are the min-imum and maximum values of the fuel equivalence ratio φ in Equa-tion 17.2-3. Equation 17.2-3 will be solved only if Equivalence RatioMinimum < φ < Equivalence Ratio Maximum; if φ is outside of thisrange, there is no soot formation.

Activation Temperature of Soot Formation Rate is the term E/R in Equa-tion 17.2-3.

Magnussen Constant for Soot Combustion is the constant A used in therate expressions governing the soot combustion rate (Equations17.2-5 and 17.2-6).

Note that the default values for these parameters are for propane fuel [39,253], and are considered to be valid for a wide range of hydrocarbon fuels.

Setting Model Parameters for the Two-Step Model

When you choose the two-step model for soot formation, the modelingparameters to be defined are those used in Equations 17.2-5, 17.2-6,17.2-9, 17.2-11, and 17.2-12:

Limiting Nuclei Formation Rate is the limiting value of the kinetic nucleiformation rate η0 in Equation 17.2-12. Below this limiting value,the branching and termination term, (f − g) in Equation 17.2-11,is not included.

Nuclei Branching-Termination Coefficient is the term (f − g) in Equa-tion 17.2-11.


17.2 Soot Formation

Nuclei Coefficient of Linear Termination on Soot is the term g0 in Equa-tion 17.2-11.

Preexponential Constant of Nuclei Formation is the pre-exponential terma0 in the kinetic nuclei formation term, Equation 17.2-12.

Activation Temperature of Nuclei Formation Rate is the term E/R in thekinetic nuclei formation term, Equation 17.2-12.

Constant Alpha for Soot Formation Rate is α, the constant in the sootformation rate equation, Equation 17.2-9.

Constant Beta for Soot Formation Rate is β, the constant in the soot for-mation rate equation, Equation 17.2-9.

Magnussen Constant for Soot Combustion is the constant A used in therate expressions governing the soot combustion rate (Equations17.2-5 and 17.2-6).

The default values for the two-step model are the same as in [149] (foran acetylene flame), except for a0, which is assumed to have the originalvalue from [242]. If your model involves propane fuel rather that acety-lene, it is recommended that you change the value of α to 3.5 × 108 [1].For best results, you should modify both of these parameters, using em-pirically determined inputs for your specific combustion system.

Defining Boundary Conditions for the Soot Model

At flow inlet boundaries, you will need to specify the Soot Mass Fraction,Ysoot, in Equation 17.2-1, and (for the two-step model only) the Nucleimass concentration, b∗nuc, in Equation 17.2-7.

Define −→Boundary Conditions...

You can retain the default inlet values of zero for both quantities or youcan input non-zero numbers as appropriate for your combustion system.



Coupled Soot Calculations

If you are calculating a coupled solution for the soot and the flow field,you will generally need to increase the convergence criteria for soot (andnuclei, for the two-step model) to 10−4. You may choose to keep therecommended value of 10−5 used for the uncoupled soot calculation, butbe aware that the coupled solution may not be able to converge to thisstricter tolerance.

For coupled calculations you should also use a lower under-relaxationfactor for soot (and nuclei, for the two-step model). A value of 0.2 willbe suitable in most cases.

If you are calculating a coupled solution and you are modeling radiativeheat transfer using a variable absorption coefficient, you should enablethe Generalized Model for Soot-Radiation Interaction in the Soot Modelpanel. When this option is enabled, FLUENT will include the effectof soot on the variable radiation absorption coefficient, as described inSection 11.3.8.

Reporting Soot Quantities

FLUENT provides several additional reporting options when your modelincludes soot formation. You can generate graphical plots or alphanu-meric reports of the following items:

• Mass fraction of soot

• Mass fraction of nuclei (for the two-step model only)

Both of these parameters are contained in the Soot... category of thevariable selection drop-down list that appears in postprocessing panels.


chapter 17. modeling pollutant formation - enea · chapter 17. modeling pollutant formation ... x...

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